paraxial equation 中文意思是什麼
paraxial equation
解釋
傍軸方程-
In chapter 2, a schrodinger formulation for paraxial light beam propagation of the real and comprehensive refractive indexes is represented. the equation for the atom laser beam wave - function is also given by a schrodinger equation, which is similar to the equation of the time - dependent system. therefore, it is possible to investigate the propagation of an atom laser beam
第二章：本章介紹了傍軸光束在實數折射率介質和復數折射率介質中傳輸的schrdinger形式理論，同時指出由於原子激光的傳輸滿足schrdinger方程，與含時量子系統的傳輸方程類似，故利用含時量子系統的schrdinger形式理論來研究原子激光的傳輸是可行的。 -
The main results achieved in this thesis can be summarized as follows : 1. by means of the fourier series expansion, an approximate analytical propagation equation of flattened gaussian beams ( fgbs ) passing through an apertured paraxial abcd optical system is derived, and illustrated with numerical examples, when the transmissivity of the aperture is t ( x ) = cos ( x )
用傅立葉級數展開法研究了平頂高斯光束通過有光闌限制的近軸abcd光學系統的傳輸特性，導出了光闌透射率為t （ x ） = cos （ x ）時的近似解析傳輸公式，硬邊光闌的情況可作為= 0的特例得到。 -
Based on this, a case of typical external self - focusing effect, hot - image, has been analytically and experimentally investigated in this dissertation. the principal work is as follows. ( 1 ) intense laser beam propagation equation, the paraxial wave equation, has been derived
論文的主要內容為如下幾部分： （ 1 ）從電磁波的基本傳播方程出發，推導了描述強激光在透明克爾介質中傳輸行為的非線性近軸波動方程。 -
( 2 ) based on the propagation equation of fgbs passing through unapertured paraxial abcd optical systems, the similar transformation conditions are obtained for the first time, which is expressed as that two fgbs with the same beam order have similar intensity distributions at the two positions of equal generalized fresnel number when they propagate through two ajb, cjdi ( i = l, 2 ) systems. furthermore, a comparison between a fob and a sgb of the same beam a ^ - factor but different waist widths is performed for the first time
（ 2 ）通過對作為整體的平頂高斯光束在無光闌限制近軸abcd光學系統中傳輸公式的分析，首次得到了平頂高斯光束的相似變換條件，即階數相同的平頂高斯光束在傳輸矩陣為a _ ib _ ic _ id _ i （ i = 1 ， 2 ）的兩個光學系統中傳輸時，在菲涅爾數相等的兩個面上具有相似的光強分佈。 -
To deal with the case of 2 dimension spatial self - focusing, it predicts the catastrophic collapse of a self - focusing beam in a kerr medium. this un - physical collapse is due to the invalidity of the paraxial wave equation in the neighborhood of a self - focus
在該理論應用於空間二維的自聚焦時，出現了光束將無限聚焦的結果，這在物理上是不可想像的，原因是在自聚焦點附近傍軸方程已經失效了。 -
Such conclusion is given : shorten the fresnel shu, shorten the obscuration ’ s area percent and shorten the equivalent diffraction distances will improve the optical quality. ( 4 ) the nonlinear paraxial equation is understood to analyze the n slabs ’ hot - image rule
得出在高功率固體激光裝置中應縮小散射點的菲涅耳數和散射面積比，控制散射點的等效衍射距離，使散射點接近等效衍射距離為零，即像面的位置。 -
In section 4, by making use of the fourier transformation for spatial variables and starting from the nonparaxial propagating equation of ultrashort pulsed beam in temporal frequency domain, the nonparaxial solution basing on the paraxial propagating solution was derived, which come to exact solution by iterative of the paraxial integral solution
在第四節里，通過採用空間變量的傅立葉變換和利用時間頻率域下的非傍軸傳輸方程，我們得出了超短脈沖光束傳輸的非傍軸的修正方法。 -
The condition, under which the paraxial approximation is valid, is given. 4. starting from the rayleigh diffraction integral, the propagation equation of ultrashort pulsed beams in dispersive media has been derived without making the paraxial approximation and slowly varying envelope approximation ( svea ), which allows for relatively large angles
從瑞利衍射積分公式出發，未作慢變振幅近似和近軸近似的條件下，導出了等衍射長度超短脈沖高斯光束在色散介質中非近軸傳輸方程，可用來處理色散介質較大角度的傳輸。 -
Starting from the collins formula, a recurrence equation of hermite - cosine - gaussian ( hcg ) beams propagating through a paraxial abcd system with a hard - edged aperture is derived, from which the analytical propagation expressions for apertured hcg beams of any order can be derived by using the recursive algorithm
從collins公式出發，推導出了厄米?餘弦?高斯光束通過有硬邊光闌近軸abcd光學系統傳輸的遞推公式。由遞推公式，藉助迭代演算法，得出受光闌限制的任意階厄米?餘弦?高斯光束的解析傳輸公式。 -
Chapter 3 : the source - dependent expansion ( sde ) method for analyzing the wave equation is introduced, which is an effective method for solving the paraxial wave equation with nonlinear source terms. two examples have been given to explain this method, which are the propagation of the ultrashort intense laser pulses propagation in the partially stripped plasma in which the collisions of plasma electrons are taken into account, and the propagation including the finite pulse length effect
第三章：本章介紹了求解有非線性源項的傍軸方程的有效方法-源展開方法，並給出了兩個具體的例子，即考慮等離子體電子間碰撞的隧道傳輸的求解和考慮激光脈沖的有限脈寬效應的隧道傳輸求解。 -
Based on the basic equation, the non - paraxial correction of pulsed beam is obtained by the spectrum analysis technic and the perturbative technic respectively. the result from the above mentioned two technics are compared to each other
基於上述方程，分別用角譜分析法和微擾法得到了脈沖光束的非傍軸修正，並對這兩種方法所得結果進行了比較。 -
Based on this, i adopt the theory of probability and statistic to establish the obscuration ’ s model ; adopt the theory of diffraction to analyze the linear propagation of obscuration ; adopt the theory of nonlinear paraxial equation to comprehend the nonlinear propagation of obscuration
基於此，本文採用概率與統計理論建立了散射點模型，並在此基礎上從衍射理論出發分析散射點的線性傳輸規律，從非線性近軸波動方程出發分析散射點的非線性傳輸規律。 -
Based on the nonlinear paraxial equation and b - t theory, a differential equation, which describes the small - scale self - focusing in gain ( loss ) media has been derived. the change rule of the maximal gain frequency, cutoff frequency and integral exponential gain have been analyzed approximately
我們首先從非線性近軸波方程出發，基於b - t理論的思想，在考慮了介質的增益（損耗）特性的情況下，推導得出了小尺度自聚焦所滿足的微分方程，並通過近似方法分析了最大增長頻率、截止空間頻率及積分指數增益等的變化規律。 -
At first, we describe the optical keer effect induced by the 3rd order nonlinear effect, then we introduce the nonlinear paraxial equation and b - t theory. after describing the approximations adopted to arrive at the paraxial equation, the limitations of b - t theory have been identified
我們首先介紹了三階非線性引起的光克爾效應，由此引出了描述非線性介質中光傳輸的近軸波方程以及用於分析小擾動增長的b - t理論，同時敘述了近軸波方程的近似條件及b - t理論的不足。 -
( 3 ) by means of expanding the aperture function into a finite sum of complex gaussian functions, the propagation of fgbs through a paraxial optical abcd system with hard - edged aperture is studied, and the approximate closed - form equations of apertured fgbs are obtained for the first time. the results obtained by using the approximate closed - form equation and collins formula are compared, and the condition under which the approximate closed - form equation is applicable is analyzed
（ 3 ）利用光闌函數的復高斯函數展開法對截斷平頂高斯光束的傳輸作了研究，首次得到了截斷平頂高斯光束在近軸abcd光學系統中傳輸時的近似解析傳輸公式，通過比較用近似傳物公式和colhns公式直接數值積分所得的結果，得出了近似公式的適用范圍。 -
Starting from maxwell ' s equations, the paraxial propagation equation of intense laser light in ionizing gases is derived and is analyzed by means of the source - dependent expantion ( sde ) method. an equation governing the evolution of the laser beam redius is obtained, based on which we analyze the ionization - modulation ( im ) instability. then, a vectorial, nonparaxial propagation equation is established, and the mechanism of energy loss during the propagation is analyzed
首先從maxwell方程組出發推導出強激光在電離氣體中傳輸的傍軸傳輸方程，利用源展開方法對傍軸傳輸方程進行分析，得到光束半徑的演化方程，從而討論傳輸過程中的電離調制不穩定性；再建立矢量非傍軸模型，並討論氣體電離產生等離子體所引起的激光能量損耗機制。 -
Chapter 3 : we find a family of solutions of the paraxial wave equation that represents ultrashort pulsed light beams propagation in free space. these pulsed beams have an arbitrary temporal form and a nearly elegant hermite - gaussian cross section, which pulsed beams we call the ultralshort pulsed elegant hermite - gaussian beams
此脈沖光束解的每個頻率分量都是eleganthermite - gaussain光束，時間脈沖的形狀是任意的，具有相同的衍射距離參數，並且可以描述短於一個光學周期的超短脈沖。 -
Chapter 3 : the influence of vectorial effect on non - paraxial propagation of pulsed beam is analysed based on the basic vectorial propagation equation of ultra - short pulsed beam in free space. on the basis of the analysis and the result of chapter 2, the vectorial non - paraxial correction of ultra - short pulsed beam is obtained
第三章：這一章在脈沖矢量傳輸基本方程的基礎上，分析了矢量效應對脈沖光束非傍軸修正的影響，並基於此分析以及第二章所得結果，得出了脈沖光束的矢量非傍軸修正。
分享友人